分数阶协整子空间的半参数估计
Semiparametric estimation of fractional cointegrating subspaces
摘要：
考虑了多元分数协整的共成分模型，其中$s\geq1$成分具有不同的记忆参数。协整秩可以超过1。我们将真正的协整向量分解成正交分数协整子空间，使得来自不同子空间的向量产生具有不同记忆参数的协整误差。我们估计每个协整子空间分别，使用适当的特征向量集的平均周期图矩阵的锥形，差分观测，第一$m$傅立叶频率的基础上，与$m$固定。真实的和估计的协整子空间之间的角度是$o_p(1)$。我们使用的协整残差对应的估计协整向量，以获得一致的和渐近正态估计的记忆参数为给定的协整子空间，使用一个单变量高斯半参数估计的带宽，往往比$n$更慢的$\infty$。我们使用这些估计来检验分数协整，并一致地确定协整子空间。
英文摘要：
We consider a common-components model for multivariate fractional cointegration, in which the $s\geq1$ components have different memory parameters. The cointegrating rank may exceed 1. We decompose the true cointegrating vectors into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters. We estimate each cointegrating subspace separately, using appropriate sets of eigenvectors of an averaged periodogram matrix of tapered, differenced observations, based on the first $m$ Fourier frequencies, with $m$ fixed. The angle between the true and estimated cointegrating subspaces is $o_p(1)$. We use the cointegrating residuals corresponding to an estimated cointegrating vector to obtain a consistent and asymptotically normal estimate of the memory parameter for the given cointegrating subspace, using a univariate Gaussian semiparametric estimator with a bandwidth that tends to $\infty$ more slowly than $n$. We use these estimates to test for fractional cointegration and to consistently identify the cointegrating subspaces.
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